WASHINGTON—The State Department received more than 2.5 million comments on whether to permit construction of the Keystone XL oil pipeline. More than 1.26 million people have weighed in this summer on Federal Communications Commission rules on how broadband providers treat traffic on their networks. At the Environmental Protection Agency, officials are sorting through hundreds of thousands of comments on new emissions rules for power plants.

Record numbers of online comments are flooding agencies at a time when Congress is...